We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

翻译：我们研究了一类离线数据驱动环境下的品类优化问题。企业未知潜在的顾客选择模型，但拥有包含历史提供的品类集、顾客选择结果及收益的离线数据集。目标在于利用离线数据集找到最优品类。由于品类优化问题具有组合性质，离线数据集中很可能出现数据覆盖不足的情况。因此，设计可证明有效的离线学习算法成为一项重要挑战。为此，我们提出了一种基于悲观主义原则设计的算法（简称PASTA），该算法在一般设定下仅需离线数据覆盖最优品类即可正确识别最优品类。特别地，我们针对经典的多项Logit模型建立了离线品类优化问题的遗憾界。同时提出了求解该悲观品类优化问题的高效计算流程。数值实验表明，所提方法相较现有基线方法具有显著优越性。